Sheet resistors having integral tap points



Dec. 31, 19.681 0. M. MAKOW SHEET RESISTORS HAVING INTEGRAL TAP POINTSFiled March 27, 1967 .OFF-AXIS CURRENT FEED United States Patent3,419,841 SHEET RESISTORS HAVING INTEGRAL TAP POINTS David Mark Makow,Ottawa, Ontario, Canada, assignor to Canadian Patents and DevelopmentLimited, Ottawa,

Ontario, Canada, a corporation of Canada Filed Mar. 27, 1967, Ser. No.626,094 9 Claims. (Cl. 338308) ABSTRACT OF THE DISCLOSURE A fixedresistor of thin sheet or film form having opposed edges, between feedpoints on which a voltage may be applied to produce current flow along acurrent axis between the points and through the body of the resistor, atleast one of these edges being shaped as an integral triangularprojection extending at 30 to 45 degrees from the current axis to apointed terminal at the tip of which the potential gradient is very lowand a voltage proportional to the applied voltage may be tapped; oneform is basically a rectangle from whose sides segments are removed toleave concave margins symmetric about the axis, permitting electricalganging of the tips of cusps bounded by the margins which are at likepotential.

This invention relates to fixed resistors, and the object I have in viewis to provide a precision sheet resistor having its margins shaped toprovide one or more integral tapping projections shaped as elongatepoints extending in directions which make acute angles with respect to acurrent flow axis, whereby the distribution of equipotential lines inthe terminal area of the point assures low potential gradients in sucharea. Resistors so constructed permit connections to be made with theends of such projections with insignificant errors in the measurement ofpotential arising from small variations in the position of theconnection at the point.

Resistors constructed according to the invention and having at least onetapping projection are useful when connected in series as voltagedivider chains to obtain precise voltage subdivision at connecting taps.

Resistors formed as symmetrical sheet bodies and having at least onepair of tapping projections according to the invention are especiallyuseful as precise meter shunts.

It is well known that resistors made from a sheet of resistive materialof uniform thickness, if exactly similar to each other in all respectsexcept the scale of their plan form, will have identical resistance fora given temperature. The resistors according to the present inventionlikewise exhibit constant resistance regardless of the scale of theirplan area, and moreover the symmetrical sheet forms of resistor exhibita substantially constant impedance which is independent of frequency upto hundreds of megacycles per second.

If a given current is passed through a flat sheet resistor shaped as asquare, along a current axis bisecting opposed sides of the square, thedistribution of current will be such that the density along the axis ishighest, falling olf to each side of the axis and being minimum alongthe other two sides. The equipotential lines may be readily plotted, thelines forming an orthogonally related pattern with the plot of currentflow lines, among which will be found a certain potential whose locusintersects the pair of corners lying on opposite sides of the currentaxis. This locus also intersects the current axis at a pointintermediate one current connection point and the midpoint of theresistor. It will also be found that on either side of thisequipotential curve in the vicinity of the corner point the gradient islower than at any other area along the margins. Nevertheless, smalldifferences in the position of a connector such as a test prod appliedto the corner will produce substantial discrepancies in potentialmeasurements.

I have found that when the margins of a sheet of resistive material arearcuately shaped to provide a resistor having two orthogonally relatedpairs of opposed concave margins, and current is passed through theresistor body so defined by way of current feed points located at theends of a current axis bisecting the sheet and also bisecting eachmargin of an opposed pair, that the plot of equipotential lines in thecusps formed by the junctions of adjacent margins exhibits very lowpotential gradient, particularly in the vicinity of the point of thecusp. When the margins have arcuate form and all have the same radius ofcurvature and are generated on centers lying equidistant from the centerof the body, a pair of centers being located on a respective axis of apair of axes which are at right angles, a highly precise resistor willbe realized, wherein either axis may be chosen as the current axis. Thepotential difference between that pair of cusps lying on the same sideof the cur-rent axis, or between either pair which lie diagonallyopposite each other, is substantially a constant fraction of the appliedvoltage at the current feed points, and will depend on the concavity ofthe margins; for example, when the margins are circularly concave asdescribed above, the voltage difference is about 28% of the appliedvoltage. The same potentiometric ratio will be obtained regardless ofthe scale to which the resistor is made, if the thickness, resistivity,and temperature are held constant over the whole area of the resistor.If a constant current is passed between the current feed points, thepotential difference established will depend on the variation of any oneparameter when the others are held constant. The resistor body may haveits concave margins defined by curves other than circular arcs; forexample, these may be defined by parabolae, hyperbolae, ellipses, or anysymmetrical oval indentation. Moreover the marginal outlines may beproduced by combinations of straight lines, disposed at various anglesin simulation of a regular curve, provided that in all forms theelongate tapering point or cusp is extended in a direction which formsan acute angle with the current axis.

Moreover, the margins of the resistor body may be generated by curves orlines so that while the body may be symmetrical if folded about thecurrent axis, it is not necessarily similar when folded about a midlinewhich is at right angles to the current axis.

Such resistors afford a high tolerance to off-axis positions of currentfeed connections, when the pair of potential differences at the ends ofrespective diagonals between cusps are averaged to provide a meandifference.

The invention may be the better understood from a reading of thefollowing description of its preferred embodiments together with theaccompanying figures of drawing, in which:

FIGURE 1 is a plan view of the resistor body according to the inventionhaving its margins geometrically defined by circular arcs, showingcurrent axis and a plot of equipotential lines;

FIGURE 2 is a cross-section taken on a transverse axis along line 22 ofFIGURE 1;

FIGURE 3 shows a similar body having its margins defined by identicalparabolae;

FIGURE 4 shows a resistor body having the margins formed by straightlines, and the tapering points extended at about 40 with respect to thecurrent axis;

FIGURE 5 shows a resistor as in FIGURE 1 wherein the position of one ofthe current feed points is displaced from the axis;

FIGURE 6 is a graph plotting error in the mean potential differenceobserved for the device of FIGURE 5;

FIGURE 7 shows a pro-assembly perspective detail of a notched currentjunction for solder connection of adjacent series-connected metal sheetresistors;

FIGURE 8 is a side elevation view of a self supporting train of metalresistors as in FIGURE 7, having a common current axis;

FIGURE 9 shows a chain of identical deposited film resistors each havinga single elongate tapering point leading to a respective tappingconnection of a precision voltage divider; and,

FIGURE 10 shows a chain similar to that of FIGURE 9 wherein eachresistor is a symmetrical body having pairs of like-potential cuspsgauged by low resistance buses.

The resistor sheet generally designated 10 in FIGURE 1 has a cur-rentaxis 11 and a transverse axis 12 intersecting at a center point 13. Theopposed margins 14, 15 are circular arcs having centers 16, 17 in theaxis 11, and the other margins 18, 19 have centers 20, 21 in the axis12. Current feed points 22 and 23 lie at the intersection of axis 11with the margins 14 and 15.

The symmetrical body 10 thus generated has four cusps, the points ofwhich are 24, 25, 26 and 27, bisected by the diagonal 28, 29. It will beapparent that the body essentially comprises the inscribed square 30indicated by dashed outline, having four like segments removed. Eachradius 1' should be one-half the distance between a pair of centersdesignated 16 and 21. The body is well adapted for precise fabricationas when a square blank sheet 30 has its margins sheared to produceconcave edges by means of circular punch and die tools, the square beingrotated about a center 13 and indexed in positions 90 apart.

The equipotential lines which may be plotted on the surface of theresistor include a curved line 31 which in tersects the axis 11 at thepoint 32, and which extends into the points of the cusps. The adjacentequipotential lines 33, 34 which run into the cusp margins at pointsspaced from the tip intersect the axis 11 at points indistinguishablyclose to the point 32, when the interval is taken as about one percentof the voltage difference between feed points 22 and 23. Consequently,tapping connections made with the point may vary appreciably in physicalposition without introducing significant error in a measurement of thepotential at the tip of the cusp.

In the device of FIGURE 3, the parabolic indentations are formed byopposed par-abolae 35. The point of each cusp lies theoretically atinfinity, but practically may be taken as the intersection of dashedlines outlining the square 30, the sides of which intersect axes 11 and12 at right angles; for example each side may be the latus rectum of aparabola. The breadth of each cusp decreases more gradually toward thetip than in the device of FIGURE 1.

The margins 14, 15 of the device of FIGURE 4 include triangularprojections 37, 38, 39, 40, having cusp points as in FIGURE 1 and thecurrent feed points 22 and 23 lie on short transverse straight lineedges. The bisectors 50 make acute angles of about 40 with the currentaxis 11. The potential difference between the cusp points which are onthe same side of the current axis or between cusps lying diagonallyopposite each other is somewhat greater in this embodiment than thedifference observed for the FIG- URE 1 embodiment, due to the increasedratio of length to width of the resistor and the smaller angle made bythe bisector 50. It will be understood that as the length of theresistor is increased in relation to the breadth as measured along thetransverse axis 12, a proportionately greater fraction of the appliedvoltage will be manifested between cusp points such as and 26. Thetriangular projections may be disposed so that their apical bisectorsform acute angles smaller or larger than 40, for example in the range to50.

While it would be expected for a precisely symmetrically shaped resistorthat the voltage differences between diagonally opposite cusp pointsshould be identical if the current feed points lie precisely on thejunction of axis 11 with the end margins, in practice some variationsare observed, due largely to the nature of the current connections. Itis extremely difiicult to make a solder connection which is a perfectlysymmetrical body of rotation about the axis 11 with a marginal edge.However as shown by FIGURES 5 and 6, the current feed points may havesubstantial off-axis positions, such as represented by a test currentleads 22A offset to the right of the ,axis by one thickness t of theresistor sheet and by the group of leads 22B-D offset to the left byunit distances each equal to twice the sheet thickness. Inspection ofthe observed variation of potential between diagonally opposed pairs ofcusp points 24-27 and 25-26 reveals that when these are averaged, theerror of the mean is far lower, and over a range of offsets equal to asmall multiple of the sheet thickness becomes negligible. Accordingly,for the highest precision of potential tapping the means potentialdifference should be relied on even though the current feed pointsappear to be accurately located. Suchaveraging also minimizes errors dueto non-homogeneity of the resistor and variations of thickness ortemperature over the area of the resistor body.

In FIGURE 7 the margins 14 and 15 are shown notched, each notch 14A and15A having a width and depth approximately equal to the thickness t ofthe sheet, the drawing exaggerating the thickness dimension for clarity.Nevertheless, metal resistors of considerable thickness may be employedin high-current, low-voltage divider trains, the thickness being notgreater than about 0.15 times the minimum breadth measured along axis12. Such junction provides a good mechanical joint and may be reinforcedby a drop of soft solder, silver solder, or brazing metal, as at 41 inFIGURE 8. The voltages between adjacent like-potential points of thetrain, designated 25, 25', 25" will show a constant difference so thatthe chain may serve as a decade resistor or in any application requiringprecise subdivision of an applied voltage in constant unit steps.

In the resistor train of FIGURE 9 each element 10A comprises an areabounded by edges each of which is comprised by a circular arc mergingwith a straight line portion. Only two diagonally opposed cusps extendfrom the body, one being formed by arcs 14A and 19, the other by arcs 18and 15. Straight line portions 14A, 18A, and 19A, 15A lie on a rectanglewith which the arcs are merged. The cusps may also be bounded by curvedlines other than circular arcs. The material coating each area may beany one of the known resistive materials that may be deposited orprinted on a supporting base sheet 43, and may include relatively thinmetallic or metal alloy films of high resistivity. Current feed pointssecured in the base sheet and permanently connected with each resistorelement comprise posts or solder electrodes 122 and 123. Similarly thecusp points 125 are provided with leads at which potentials may bemeasured along the train. It will be evident that the resistor body 10Ais neither symmetrical if folded about the current axis or about atransverse axis through the midpoint of the resistor. Nevertheless, thepotential gradient in the vicinity of the point of the cusp will be lowso that readings of voltage will be relatively accurate.

The resistor films may be deposited as a group by known printingtechniques, even when the physical dimensions of the resistors areextremely small, so that a relatively precise voltage divider system maybe realized at low cost. It is to be noted that the terminal body 125may comprise a relatively broad low-resistance metal post or depositedconductor spot, connected with the pointed extremity of the cusp portionso that external connections cannot introduce gradient error.

In the train of FIGURE 10, the elements are either stamped conductivesheets or printed films, provided with an axis of symmetry 11 and theelements being spaced to avoid interference between their cusps, andhaving lowresistance bus or metal connector deposits 44 joined betweentheir current feed points. Similarly, and preferably on that side of thebase sheet opposite to the side along which the current connections areled, the pair of likepotential cusp points are ganged by transverselow-resistance conductors 45. Such train will obviously permit a greatercurrent to be tapped at the cusp points without affecting the potentialdistribution. While the particular embodiment shown comprises elementshaving concave margins of like radius and the potentials are indicatedalong the train for such form of elements, it is to be understood thatany of the forms described herinabove having symmetry about the currentaxis may be used.

It is to be understood that the surface area of each resistor elementshould be chosen to provide adequate heat dissipation. Since theresistance of the element is a parameter independent of the scale inplan, provided thickness and resistivity is held constant, it will beevident that extremely small area elements made of uniformly thin filmsof high resistivity may be fabricated having resistance values from afraction of an ohm to hundreds or thousands of ohms. As the scale of theelement is reduced, the accuracy of the tapping connections becomesinherently greater by comparison with prior resistor forms.

I claim:

1. A fixed resistor of sheet form having a pair of opposed marginaledges provided with current feed points defining a current axis betweensaid points, at least one of said marginal edges being extended as apointed tapping projection at an acute angle with respect to said axis.

2. A fixed resistor as set forth in claim 1 wherein said projection isextended at an angle in the range of 30 to 45 degrees and the bisectorof said projection intersects said current axis at a point intermediatesaid current feed points.

3. A fixed resistor as set forth in claim 2 wherein said tappingprojection is bounded by concavely recessed marginal edges of saidresistor,

4. A fixed resistor as set forth in claim 3 having the form of arectangle from each side of which a convex segment has been removed toform a concavely curved marginal edge and wherein said resistor issymmetrical about said current axis.

5. A fixed resistor as set forth in claim 4 wherein said curved marginaledges are defined by circular arcs.

6. A fixed resistor as set forth in claim 3 formed as a self-supportinghomogenous body having a parallel-sided recess formed at each currentfeed point, the sides of the recess being spaced to permit axialengagement of the resistor with another in interlocking relation.

7. A fixed resistor as set 'forth in claim 3 wherein each element of atrain of series-connected resistors comprises a film of resistivematerial adhered to a common supporting base.

8. A fixed resistor as set forth in claim 4 wherein the points oftapping projections lying opposite each other with respect to saidcurrent axis are electrically ganged by a conductor.

9. A fixed resistor as set forth in claim 8 wherein said resistor issymmetrical about an axis at right angles to said current axis.

References Cited UNITED STATES PATENTS 2,994,848 8/1961 Rayburn 338-3283,325,763 6/1967 Casey 338309 3,379,858 4/1968 Peters 219522 VOLODYMYRY. MAYEWSKY, Primary Examiner.

U.S. Cl. X.R.

